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Dynamic deformation events induced by osmosis or photochemical stiffening substantially influence geometrical and mechanical assessments in post-mortem corneas, therefore need to be carefully monitored in experimental settings. In this study, we employed optical coherence elastography (OCE) to quantify dynamic deformation processes at high resolution in freshly enucleated porcine corneas. Osmotic effects were studied by immerging n = 9 eyes in preservation media of three different tonicities. Dynamic processes underlying corneal cross-linking (CXL) were studied by subjecting n = 6 eyes to standard Dresden treatment, while three control groups were used. The entire procedures were performed under an OCE setup during up to 80 min, acquiring a volumetric scan every 20 s. Changes in OCE-derived axial deformations were incrementally calculated between consecutive scans. Preservation conditions had a strong influence on the observed strain patterns, which were consistent with the tonicity of the medium (swelling in hypotonic, deswelling in hypertonic environment). In the CXL group, we observed deswelling of the anterior stroma 10 min after starting the UV irradiation, which was not observed in any control group (p = 0.007). The presented results proved OCE to be a valuable technique to quantify subtle dynamic biomechanical alterations in the cornea resulting from CXL and preservation solutions.

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A hallmark of Alzheimer's disease (AD) is cholinergic system dysfunction, directly affecting the hippocampal neurons. Previous experiments have demonstrated that reduced complexity is one significant effect of AD on electroencephalography (EEG). Motivated by these, this study explores reduced EEG complexity of cholinergic deficiency in AD by neurocomputation. We first construct a new hippocampal CA1 circuit model with cholinergic action. M-current IM and calcium-activated potassium current IAHP are newly introduced in the model to describe cholinergic input from the medial septum. Then, by enhancing IM and IAHP to mimic cholinergic deficiency, how cholinergic deficiency influences the model complexity is investigated by sample entropy (SampEn) and approximate entropy (ApEn). Numerical results show a more severe cholinergic deficit with lower model complexity. Furthermore, we conclude that the decline of SampEn and ApEn is due to the greatly diminished excitability of model neurons. These suggest that decreased neuronal excitability due to cholinergic impairment may contribute to reduced EEG complexity in AD. Subsequently, statistical analysis between simulated AD patients and normal control (NC) groups demonstrates that SampEn and auto-mutual-information (AMI) decrease rates significantly differ. Compared to NC, AD patients have a lower SampEn and a less negative AMI decline rate. These imply a low rate of new-generation information in AD brains with cholinergic deficits. Interestingly, the statistical correlation between SampEn and AMI is analyzed, and they have a large negative Pearson correlation coefficient. Thus, AMI reduction rates may be a complementary tool for complex analysis. Our modeling and complex analysis are expected to provide a deeper understanding of the reduced EEG complexity resulting from cholinergic deficiency.

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This study explores the inherent nonlinearity of quarter car models by employing an experimental and numerical approach. The dynamics of vehicular suspension systems are pivotal for ensuring passenger comfort, vehicle stability, and overall ride quality. In this paper we assessed the impact of various parameters and components on suspension performance, enabled the optimization of ride comfort, stability, and handling characteristics. Firstly, experimental analysis allowed for the investigation of factors that are challenging to model theoretically, such as stiffness nonlinearity and damping characteristics, which may vary under different operating conditions. Time domain and frequency response diagram of the model has been obtained. Secondly, a quarter-car with single degree-of-freedom presented and investigated in fractional order form. Fractional order dynamics emphasize nonlinearities in quarter car models, capturing real-world dynamics effectively. The proposed fractional-order nonlinear quarter car model employed Caputo derivative. For numerical analysis of fractional order system, the Adam-Bashforth-Moulton method is used and the disturbance of road assumed to be stochastic. Results show that the dynamic response of the vehicle can be chaotic. Influence of road roughness amplitude and frequency on vehicle vibration is investigated.

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Studying simple chaotic systems with fractional-order derivatives improves modeling accuracy, increases complexity, and enhances control capabilities and robustness against noise. This paper investigates the dynamics of the simple Sprott-B chaotic system using fractional-order derivatives. This study involves a comprehensive dynamical analysis conducted through bifurcation diagrams, revealing the presence of coexisting attractors. Additionally, the synchronization behavior of the system is examined for various derivative orders. Finally, the integer-order and fractional-order electronic circuits are implemented to validate the theoretical findings. This research contributes to a deeper understanding of the Sprott-B system and its fractional-order dynamics, with potential applications in diverse fields such as chaos-based secure communications and nonlinear control systems.

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Different movement speeds can contribute to different joint loading in sports. Joint contact force is the actual force acting on the articular surface, which could predict performance and injury, but is rarely reported for badminton overhead strokes. Through an approach using musculoskeletal modelling, six male elite badminton players performed forehand overhead strokes at different movement speeds (fast (100%) vs. moderate (90%)). The synchronized kinematics and ground reaction force (GRF) data were measured using a motion capturing system and a force platform. All kinematics and GRF information were input into the AnyBody musculoskeletal modelling to determine the three-dimensional hip, knee and ankle contact forces. Paired t-tests were performed to assess the significant differences among the GRF, joint kinematics and contact force variables between the movement speed conditions. The results showed that when compared with the moderate movement condition, participants performing faster stroke movements induced larger first and second vertical peaks and larger first horizontal peak but lower second horizontal peak, and it also led to higher peak ankle lateral and distal contact forces, knee lateral and distal contact forces, and hip distal contact forces. Additionally, fast movements corresponded with distinct joint angles and velocities at the instant of initial contact, peak and take-off among the hip, knee and ankle joints compared with moderate movement speeds. The current results suggest that changes in joint kinematics and loading could contribute to changes in movement speeds. However, the relationship between lower limb joint kinematics and contact forces during overhead stroke is unclear and requires further investigation.

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To explore the crossover linkage of the bacterial infections resulting from the viral infection, within the host body, a computational framework is developed. It analyzes the additional pathogenic effect of Streptococcus pneumonia, one of the bacteria that can trigger the super-infection mechanism in the COVID-19 syndrome and the physiological effects of innate immunity for the control or eradication of this bacterial infection. The computational framework, in a novel manner, takes into account the action of pro-inflammatory and anti-inflammatory cytokines in response to the function of macrophages. A hypothetical model is created and is transformed to a system of non-dimensional mathematical equations. The dynamics of three main parameters (macrophages sensitivity κ , sensitivity to cytokines η and bacterial sensitivity ϵ ), analyzes a "threshold value" termed as the basic reproduction number R 0 which is based on a sub-model of the inflammatory state. Piece-wise differentiation approach is used and dynamical analysis for the inflammatory response of macrophages is studied in detail. The results shows that the inflamatory response, with high probability in bacterial super-infection, is concomitant with the COVID-19 infection. The mechanism of action of the anti-inflammatory cytokines is discussed during this research and it is observed that these cytokines do not prevent inflammation chronic, but only reduce its level while increasing the activation threshold of macrophages. The results of the model quantifies the probable deficit of the biological mechanisms linked with the anti-inflammatory cytokines. The numerical results shows that for such mechanisms, a minimal action of the pathogens is strongly amplified, resulting in the "chronicity" of the inflammatory process.

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The pandemic caused by the SARS-CoV2 virus has prompted research into new therapeutic solutions that can be used to treat the CoVid-19 syndrome. As part of this research, immunotherapy, first developed against cancer, is offering new therapeutic horizons also against viral infections. CAR technology, with the production of CAR-T cells (adoptive immunotherapy), has shown applicability in the field of HIV viral infections through second generation CAR-T cells implemented with the "CD4CAR" system with a viral fusion inhibitor. In addition, to avoid the immunoescape of the virus, bi- or trispecific CAR receptors have been developed. Our research group hypothesizes the use of this immunotherapy system against SARS-CoV2, admitting the appropriate adjustments concerning the target-epitope and a possible remodeling of the nuclease related to the action of this virus. For a more in-depth analysis of this hypothesis, a mathematical model has been developed which, starting from the fractional derivative Caputo, creates a system of equations that describes the interactions between CAR-T cells, memory cells, and cells infected with SARS-CoV2. Through an analysis of the existence and non-negativity of the solutions, the hypothesis is stabilized; then is further demonstrated through the use of the piece-wise derivative and the consequent application of the formula of Newton polynomial interpolation.

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Individual specialization and generalization refer to the breadth of prey types consumed by predators among all available prey. The ecological factors mechanistically determining individual differences and the coexistence of foraging strategies remain to be clarified. Formal quantitative models can elucidate the complex nonlinear mechanisms underlying predator-prey interactions. In this study, we built a dynamical model with multiple prey, with different nutritional values and reproductive rates, which are consumed by specialist and generalist predators. We then analyzed the viability of individual foraging strategies in all possible scenarios. Relative prey fertility and relative efficiency of predation, rather than prey nutritional value, determined the success of specialists and generalists. Less reproducing prey and the specialists relying on them face the highest danger of extinction, while generalists cannot thrive where specialists are sufficiently efficient in relation to the number of available prey. Our study provides new perspectives for empirical studies on individual specialization.

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Breast cancer is a very frequent type of cancer and much attention is paid to therapy with considerable efforts both in the pharmacological and clinical fields.The present work aims to create a non-linear dynamic model of action of the drug Trastuzumab against HER-2 + breast cancer, mainly considering its action of ADCP (antibody-dependent phagocytosis) killing of cancer cells. The model, while also considering the other therapeutic effects induced by Trastuzumab, shows how the action of this monoclonal antibody in the induction of ADCP through the action of macrophages, is strictly connected to the formation of a multi-complex "Trastuzumab -HER-2 - macrophage" that shows a prolonged action over time, responsible for the increase in the Overall Survivor (OS) parameter reported in various. The model shows the correlation between the various therapeutic effects and the killing action of cancer cells through the variation of the dynamic fluctuation of the representative "c" parameter.

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Since 2019, entire world is facing the accelerating threat of Corona Virus, with its third wave on its way, although accompanied with several vaccination strategies made by world health organization. The control on the transmission of the virus is highly desired, even though several key measures have already been made, including masks, sanitizing and disinfecting measures. The ongoing research, though devoted to this pandemic, has certain flaws, due to which no permanent solution has been discovered. Currently different data based studies have emerged but unfortunately, the pandemic fate is still unrevealed. During this research, we have focused on a compartmental model, where delay is taken into account from one compartment to another. The model depicts the dynamics of the disease relative to time and constant delays in time. A deep learning technique called "Self Organizing Map" is used to extract the parametric values from the data repository of COVID-19. The input we used for SOM are the attributes on which, the variables are dependent. Different grouping/clustering of patients were achieved with 2- dimensional visualization of the input data ( h t t p s : / / c r e a t i v e c o m m o n s . o r g / l i c e n s e s / b y / 2.0 / ). Extensive stability analysis and numerical results are presented in this manuscript which can help in designing control measures.

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Structures of genetic regulatory networks are not fixed. These structural perturbations can cause changes to the reachability of systems' state spaces. As system structures are related to genotypes and state spaces are related to phenotypes, it is important to study the relationship between structures and state spaces. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. Therefore, Difference in Reachability between State Spaces (DReSS) is proposed. DReSS index family can quantitively describe differences of reachability, attractor sets between two state spaces and can help find the key structure in a system, which may influence system's state space significantly. First, basic properties of DReSS including non-negativity, symmetry and subadditivity are proved. Then, typical examples are shown to explain the meaning of DReSS and the differences between DReSS and traditional graph distance. Finally, differences of DReSS distribution between real biological regulatory networks and random networks are compared. Results show most structural perturbations in biological networks tend to affect reachability inside and between attractor basins rather than to affect attractor set itself when compared with random networks, which illustrates that most genotype differences tend to influence the proportion of different phenotypes and only a few ones can create new phenotypes. DReSS can provide researchers with a new insight to study the relation between genotypes and phenotypes.

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In this paper, dynamical behavior and synchronization of a non-equilibrium four-dimensional chaotic system are studied. The system only includes one constant term and has hidden attractors. Some dynamical features of the governing system, such as invariance and symmetry, the existence of attractors and dissipativity, chaotic flow with a plane of equilibria, and offset boosting of the chaotic attractor, are stated and discussed and a new disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method with input saturation is proposed for the control and synchronization of the chaotic system. To deal with unexpected noises, an extended Kalman filter (EKF) is implemented along with the designed controller. Through the concept of Lyapunov stability, the proposed control technique guarantees the finite time convergence of the uncertain system in the presence of disturbances and control input limits. Furthermore, to decrease the chattering phenomena, a genetic algorithm is used to optimize the controller parameters. Finally, numerical simulations are presented to demonstrate the performance of the designed control scheme in the presence of noise, disturbances, and control input saturation.

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Understanding ecological processes and predicting long-term dynamics are ongoing challenges in ecology. To address these challenges, we suggest an approach combining mathematical analyses and Bayesian hierarchical statistical modeling with diverse data sources. Novel mathematical analysis of ecological dynamics permits a process-based understanding of conditions under which systems approach equilibrium, experience large oscillations, or persist in transient states. This understanding is improved by combining ecological models with empirical observations from a variety of sources. Bayesian hierarchical models explicitly couple process-based models and data, yielding probabilistic quantification of model parameters, system characteristics, and associated uncertainties. We outline relevant tools from dynamical analysis and hierarchical modeling and argue for their integration, demonstrating the value of this synthetic approach through a simple predator-prey example.

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In December 2019, an atypical pneumonia invaded the city of Wuhan, China, and the causative agent of this disease turned out to be a new coronavirus. In January 2020, the World Health Organization named the new coronavirus 2019-nCoV and subsequently it is referred to as SARS-CoV2 and the related disease as CoViD-19 (Lai et al., 2020). Very quickly, the epidemic led to a pandemic and it is now a worldwide emergency requiring the creation of new antiviral therapies and a related vaccine. The purpose of this article is to review and investigate further the molecular mechanism by which the SARS-CoV2 virus infection proceeds via the formation of a hetero-trimer between its protein S, the ACE2 receptor and the B0AT1 protein, which is the "entry receptor" for the infection process involving membrane fusion (Li et al., 2003). A reverse engineering process uses the formalism of the Hill function to represent the functions related to the dynamics of the biochemical interactions of the viral infection process. Then, using a logical evaluation of viral density that measures the rate at which the cells are hijacked by the virus (and they provide a place for the virus to replicate) and considering the "time delay" given by the interaction between cell and virus, the expected duration of the incubation period is predicted. The conclusion is that the density of the virus varies from the "exposure time" to the "interaction time" (virus-cells). This model can be used both to evaluate the infectious condition and to analyze the incubation period. BACKGROUND: The ongoing threat of the new coronavirus SARS-CoV2 pandemic is alarming and strategies for combating infection are highly desired. This RNA virus belongs to the ß-coronavirus genus and is similar in some features to SARS-CoV. Currently, no vaccine or approved medical treatment is available. The complex dynamics of the rapid spread of this virus can be demonstrated with the aid of a computational framework. METHODS: A mathematical model based on the principles of cell-virus interaction is developed in this manuscript. The amino acid sequence of S proein and its interaction with the ACE-2 protein is mimicked with the aid of Hill function. The mathematical model with delay is solved with the aid of numerical solvers and the parametric values are obtained with the help of MCMC algorithm. RESULTS: A delay differential equation model is developed to demonstrate the dynamics of target cells, infected cells and the SARS-CoV2. The important parameters and coefficients are demonstrated with the aid of numerical computations. The resulting thresholds and forecasting may prove to be useful tools for future experimental studies and control strategies. CONCLUSIONS: From the analysis, I is concluded that control strategy via delay is a promising technique and the role of Hill function formalism in control strategies can be better interpreted in an inexpensive manner with the aid of a theoretical framework.

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Vaccination is an effective method to prevent the spread of infectious diseases. In this paper, we develop an SIVS epidemic model with degree-related transmission rates and imperfect vaccination on scale-free networks. Firstly, we derive two threshold parameters and existence conditions of multiple endemic equilibria. Secondly, not only the global asymptotical stability of disease-free equilibrium and the persistence of the disease are derived, but also the global attractivity of the unique endemic equilibrium is proved using the monotone iterative technique. Thirdly, the effects of various immunization schemes including uniform immunization, targeted immunization and acquaintance immunization are studied, and the optimal vaccination strategy is analyzed by Pontryagin's maximum principle. Finally, we perform numerical simulations to verify these theoretical results.

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BACKGROUND: The genetic control strategies of vector borne diseases includes the replacement of a vector population by "disease-refractory" mosquitoes and the release of mosquitoes with a gene to control the vector's reproduction rates. Wolbachia are common intracellular bacteria that are found in arthropods and nematodes. Wolbachia infected male mosquitos have been used in different experimental trials around the world to suppress the target population of Aedes aegypti and this genetic control strategy has proved to be a promising alternative to other treatment strategies. Due to certain limitations, the successful application of this strategy is still awaited. METHODS: Mathematical frame work for Wolbachia induced genetic control strategy has been developed in this article. With the aid of Artificial Intelligence (AI) tools, accurate parametric values are depicted. For the first time, the model is well synchronized with the experimental findings. The model is comprised of the generalized varying coefficient and multiple mating rates between infected and uninfected compartments of Aedes aegypti dengue to forecast the disease control. RESULTS: Two mathematical models are developed in this article to demonstrate different mating rates of the genetic control strategy. The important parameters and time varying coefficients are well demonstrated with the aid of numerical computations. The resulting thresholds and forecasting may prove to be a useful tool for future experimental studies. CONCLUSIONS: From our analysis, we have concluded that the genetic control strategy is a promising technique and the role of Wolbachia infected male mosquitos, in genetic control strategies, can be better interpreted in an inexpensive manner with the aid of a theoretical model.

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The ongoing threat of Coronavirus is alarming. The key players of this virus are modeled mathematically during this research. The transmission rates are hypothesized, with the aid of epidemiological concepts and recent findings. The model reported is extended, by taking into account the delayed dynamics. Time delay reflects the fact that the dynamic behavior of transmission of the disease, at time t depends not only on the state at time t but also on the state in some period τ before time t. The research presented in this manuscript will not only help in understanding the current threat of pandemic (SARS-2), but will also contribute in making precautionary measures and developing control strategies.

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Through a detailed mathematical analysis we seek to advance our understanding of how cardiac tissue conductances govern pivoting (spiral, scroll, rotor, functional reentry) wave dynamics. This is an important problem in cardiology since pivoting waves likely underlie most reentrant tachycardias. The problem is complex, and to advance our methods of analysis we introduce two new tools: a ray tracing method and a moving-interface model. When used in combination with an ionic model, they permit us to elucidate the role played by tissue conductances on pivoting wave dynamics. Specifically we simulate traveling electrical waves with an ionic model that can reproduce the characteristics of plane and pivoting waves in small patches of cardiac tissue. Then ray tracing is applied to the simulated pivoting waves in a manner to expose their real displacement. In this exercise we find loci with special characteristics, as well as zones where a part of a pivoting wave quickly transitions from a regenerative to a non-regenerative propagation mode. The loci themselves and the monitoring of the ionic model state variables in this zone permit to elucidate several aspects of pivoting wave dynamics. We then formulate the moving-interface model based on the information gathered with the above-mentioned analysis. Equipped with a velocity profile v(s), s: distance along of the pivoting wave contour and the steady- state action potential duration (APD) of a plane wave during entrainment, APDss(T), at period T, this simple model can predict: shape, orbit of revolution, rotation period, whether a pivoting wave will break up or not, and whether the tissue will admit pivoting waves or not. Because v(s) and APDss(T) are linked to the ionic model, dynamical analysis with the moving-interface model conveys information on the role played by tissue conductances on pivoting wave dynamics. The analysis conducted here enables us to better understand previous results on the termination of pivoting waves. We surmise the method put forth here could become a means to discover how to alter tissue conductances in a manner to terminate pivoting waves at the origin of reentrant tachycardias.

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The uniformly pseudo-projection-anti-monotone (UPPAM) neural network model, which can be considered as the unified continuous-time neural networks (CNNs), includes almost all of the known CNNs individuals. Recently, studies on the critical dynamics behaviors of CNNs have drawn special attentions due to its importance in both theory and applications. In this paper, we will present the analysis of the UPPAM network under the general critical conditions. It is shown that the UPPAM network possesses the global convergence and asymptotical stability under the general critical conditions if the network satisfies one quasi-symmetric requirement on the connective matrices, which is easy to be verified and applied. The general critical dynamics have rarely been studied before, and this work is an attempt to gain an meaningful assurance of general critical convergence and stability of CNNs. Since UPPAM network is the unified model for CNNs, the results obtained here can generalize and extend the existing critical conclusions for CNNs individuals, let alone those non-critical cases. Moreover, the easily verified conditions for general critical convergence and stability can further promote the applications of CNNs.

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OBJECTIVE: To explore the electroencephalogram (EEG) characteristics in patients with chronic fatigue syndrome (CFS) using brain electrical activity mapping (BEAM) and EEG nonlinear dynamical analysis. METHODS: Forty-seven outpatients were selected over a 3-month period and divided into an observation group (24 outpatients) and a control group (23 outpatients) by using the non-probability sampling method. All the patients were given a routine EEG. The BEAM and the correlation dimension changes were analyzed to characterize the EEG features. RESULTS: 1) BEAM results indicated that the energy values of δ, θ, and α1 waves significantly increased in the observation group, compared with the control group (P<0.05, P<0.01, respectively), which suggests that the brain electrical activities in CFS patients were significantly reduced and stayed in an inhibitory state; 2) the increase of δ, θ, and α1 energy values in the right frontal and left occipital regions was more significant than other encephalic regions in CFS patients, indicating the region-specific encephalic distribution; 3) the correlation dimension in the observation group was significantly lower than the control group, suggesting decreased EEG complexity in CFS patients. CONCLUSION: The spontaneous brain electrical activities in CFS patients were significantly reduced. The abnormal changes in the cerebral functions were localized at the right frontal and left occipital regions in CFS patients.